An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. The ratio most commonly used is 10. An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ... Categories: Orders of magnitude (area) ... To help compare different orders of magnitude, the following list describes various angular velocity levels between 1×10−7 rad·s−1 and 1×107 rad·s−1. ... This is a list of orders of magnitude for data (or information), measured in bits. ... Conversion Calculator for Units of Density Category: ... To help compare different orders of magnitude, the following list describes various frequencies. ... Categories: | ... Category: ... This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities. ... This page lists examples of the power in watts produced by various different sources of energy. ... 1 At earth mean sea level. ... This is a table of specific heat capacities by magnitude. ... To help compare different orders of magnitude, the following list describes various speed levels between 1. ... Circumstances where water naturally occurs in liquid form are shown in light grey. ... The pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). ... The pages linked in the right-hand column contain lists of volumes that are of the same order of magnitude (power of ten). ... Conversion of units refers to conversion factors between different units of measurement for the same quantity. ... The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The SI system of units defines seven SI base units: physical units defined by an operational definition. ... SI derived units are part of the SI system of measurement units and are derived from the seven SI base units. ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ... A scale is either a device used for measurement of weights, or a series of ratios against which different measurements can be compared. ... The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs. ... Diagram showing the geometric series 1 + 1/2 + 1/4 + 1/8 + ... which converges to 2. ...

Orders of magnitude are generally used to make very approximate comparisons. If two numbers differ by one order of magnitude, one is about ten times larger than the other. If they differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value. In mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. ... 100 (one hundred) (the Roman numeral is C for centum) is the natural number following 99 and preceding 101. ...

The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number. More precisely, the order of magnitude of a number can be defined in terms of the common logarithm, usually as the integer part of the logarithm, obtained by truncation. For example, 4,000,000 has a logarithm of 6.602; its order of magnitude is 6. When truncating, a number of this order of magnitude is between 10⁶ and 10⁷. In a similar example, "He had a seven-figure income", the order of magnitude is the number of figures minus one, so it is very easily determined without a calculator to be 6. An order of magnitude is an approximate position on a logarithmic scale. In mathematics, the common logarithm is the logarithm with base 10. ... The integers are commonly denoted by the above symbol. ... In mathematics, truncation is the term used for reducing the number of digits right of the decimal point, by discarding the least significant ones. ... A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ...

An order of magnitude estimate of a variable whose precise value is unknown is an estimate rounded to the nearest power of ten. For example, an order of magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. In other words; when rounding its logarithm, a number of order of magnitude 10 is in between 10^9.5 and 10^10.4. An order of magnitude estimate is sometimes also called a zeroth order approximation. Rounding is the process of reducing the number of significant digits in a number. ... This article is about modern humans. ... This article is about Earth as a planet. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... Often in science, engineering, or other quantitative disciplines, it is necessary to make approximations with various degrees of precision. ...

An order of magnitude difference between two values is a factor of 10. For example, the mass of the planet Saturn is 95 times that of Earth, so Saturn is two orders of magnitude more massive than Earth. Adjectives: Saturnian Atmosphere [3] Scale height: 59. ... This article is about Earth as a planet. ...

The pages in the table at right contain lists of items that are of the same order of magnitude in various units of measurement. This is useful for getting an intuitive sense of the comparative scale of familiar objects. The former Weights and Measures office in Middlesex, England. ... A scale is either a device used for measurement of weights, or a series of ratios against which different measurements can be compared. ...

Non-decimal orders of magnitude

Other orders of magnitude may be calculated using other bases than 10. The different decimal numeral systems of the world use a larger base to better envision the size of the number, and have created names for the powers of this larger base. The table shows what number the order of magnitude aim at for base 10 and for base 1000000. It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2 and tri- means 3, and the suffix -illion tells that the base is 1000000. But the number names billion, trillion themselves (here with other meaning than in the first chapter) are not names of the orders of magnitudes, they are names of "magnitudes", that is the numbers 1 000000 000000 etc. The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ... A numeral is a symbol or group of symbols that represents a number. ... Many numeral systems with base 10 use a superimposed larger base of 100, 1000, 10000 or 1000000. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term échelle courte. ...

SI units in the table at right are used together with SI prefixes, which were devised with mainly base 1000 magnitudes in mind. The IEC standard prefixes with base 1024 was invented for use in context of electronic technology. In mathematics, the common logarithm is the logarithm with base 10. ... Many numeral systems with base 10 use a superimposed larger base of 100, 1000, 10000 or 1000000. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... // In computing, binary prefixes can be used to quantify large numbers where powers of two are more useful than powers of ten (such as computer memory sizes). ...

The ancient apparent magnitudes for the brightness of stars uses the base and is reversed. The modernized version has however turned into a logarithmic scale with non-integer values. The apparent magnitude (m) of a star, planet or other celestial body is a measure of its apparent brightness as seen by an observer on Earth. ...

Extremely large numbers

For extremely large numbers, a generalized order of magnitude can be based on their double logarithm or super-logarithm. Rounding these downward to an integer gives categories between very "round numbers", rounding them to the nearest integer and applying the inverse function gives the "nearest" round number. This article or section is not written in the formal tone expected of an encyclopedia article. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... Tetration (also exponential map, hyperpower, power tower, super-exponentiation, and hyper4) is iterated exponentiation, the first hyper operator after exponentiation. ...

The double logarithm yields the categories:

..., 1.0023-1.023, 1.023-1.26, 1.26-10, 10-10¹⁰, 10¹⁰-10¹⁰⁰, 10¹⁰⁰-10¹⁰⁰⁰, ...

(the first two mentioned, and the extension to the left, may not be very useful, they merely demonstrate how the sequence mathematically continues to the left).

The super logarithm yields the categories:

, or

negative numbers, 0-1, 1-10, 10-1e10, 1e10-10^1e10, 10^1e10-10^^4, 10^^4-10^^5, etc. (see tetration)

The "midpoints" which determine which round number is nearer are in the first case: Tetration (also exponential map, hyperpower, power tower, super-exponentiation, and hyper4) is iterated exponentiation, the first hyper operator after exponentiation. ...

1.076, 2.071, 1453, 4.20e31, 1.69e316,...

and, depending on the interpolation method, in the second case

-.301, .5, 3.162, 1453, 1e1453, 10^1e1453, 10^^2@1e1453,... (see notation of extremely large numbers)

For extremely small numbers (in the sense of close to zero) neither method is suitable directly, but of course the generalized order of magnitude of the reciprocal can be considered. This article or section is not written in the formal tone expected of an encyclopedia article. ... The reciprocal function: y = 1/x. ...

Similar to the logarithmic scale one can have a double logarithmic scale (example provided here) and super-logarithmic scale. The intervals above all have the same length on them, with the "midpoints" actually midway. More generally, a point midway between two points corresponds to the generalised f-mean with f(x) the corresponding function log log x or slog x. In the case of log log x, this mean of two numbers (e.g. 2 and 16 giving 4) does not depend on the base of the logarithm, just like in the case of log x (geometric mean, 2 and 8 giving 4), but unlike in the case of log log log x (4 and 65536 giving 16 if the base is 2, but different otherwise). A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ... This is the timeline of the Universe from Big Bang to Heat Death scenario. ... In mathematics and statistics, the generalised f-mean is the natural generalisation of the more familar means such as the arithmetic mean and the geometric mean, using a function f(x). ... The geometric mean of a collection of positive data is defined as the nth root of the product of all the members of the data set, where n is the number of members. ...

See also

• Orders of approximation
• Powers of Ten
• Orders of magnitude (numbers)
• Big O notation

Often in science, engineering, or other quantitative disciplines, it is necessary to make approximations with various degrees of precision. ... Powers of Ten is a 1977 short documentary film written and directed by Charles Eames and his wife, Ray. ... This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities. ... Big O notation is often used to describe how the size of the input data affects an algorithms running time. ...

External links

• Powers of 10, a graphic animated illustration that starts with a view of the Milky Way at 10²³ meters and ends with subatomic particles at 10^-16 meters.
• Orders of Magnitude - Distance
• What is Order of Magnitude?